Actual source code: ex3.c


  2: static char help[] ="Model Equations for Advection-Diffusion\n";

  4: /*
  5:     Page 9, Section 1.2 Model Equations for Advection-Diffusion

  7:           u_t = a u_x + d u_xx

  9:    The initial conditions used here different then in the book.

 11: */

 13: /*
 14:      Helpful runtime linear solver options:
 15:            -pc_type mg -da_refine 2 -snes_monitor -ksp_monitor -ts_view   (geometric multigrid with three levels)

 17: */

 19: /*
 20:    Include "petscts.h" so that we can use TS solvers.  Note that this file
 21:    automatically includes:
 22:      petscsys.h       - base PETSc routines   petscvec.h  - vectors
 23:      petscmat.h  - matrices
 24:      petscis.h     - index sets            petscksp.h  - Krylov subspace methods
 25:      petscviewer.h - viewers               petscpc.h   - preconditioners
 26:      petscksp.h   - linear solvers        petscsnes.h - nonlinear solvers
 27: */

 29: #include <petscts.h>
 30: #include <petscdm.h>
 31: #include <petscdmda.h>

 33: /*
 34:    User-defined application context - contains data needed by the
 35:    application-provided call-back routines.
 36: */
 37: typedef struct {
 38:   PetscScalar a,d;   /* advection and diffusion strength */
 39:   PetscBool   upwind;
 40: } AppCtx;

 42: /*
 43:    User-defined routines
 44: */
 45: extern PetscErrorCode InitialConditions(TS,Vec,AppCtx*);
 46: extern PetscErrorCode RHSMatrixHeat(TS,PetscReal,Vec,Mat,Mat,void*);
 47: extern PetscErrorCode Solution(TS,PetscReal,Vec,AppCtx*);

 49: int main(int argc,char **argv)
 50: {
 51:   AppCtx         appctx;                 /* user-defined application context */
 52:   TS             ts;                     /* timestepping context */
 53:   Vec            U;                      /* approximate solution vector */
 55:   PetscReal      dt;
 56:   DM             da;
 57:   PetscInt       M;

 59:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 60:      Initialize program and set problem parameters
 61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 63:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 64:   appctx.a      = 1.0;
 65:   appctx.d      = 0.0;
 66:   PetscOptionsGetScalar(NULL,NULL,"-a",&appctx.a,NULL);
 67:   PetscOptionsGetScalar(NULL,NULL,"-d",&appctx.d,NULL);
 68:   appctx.upwind = PETSC_TRUE;
 69:   PetscOptionsGetBool(NULL,NULL,"-upwind",&appctx.upwind,NULL);

 71:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC, 60, 1, 1,NULL,&da);
 72:   DMSetFromOptions(da);
 73:   DMSetUp(da);
 74:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 75:      Create vector data structures
 76:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 78:   /*
 79:      Create vector data structures for approximate and exact solutions
 80:   */
 81:   DMCreateGlobalVector(da,&U);

 83:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 84:      Create timestepping solver context
 85:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 87:   TSCreate(PETSC_COMM_WORLD,&ts);
 88:   TSSetDM(ts,da);

 90:   /*
 91:       For linear problems with a time-dependent f(U,t) in the equation
 92:      u_t = f(u,t), the user provides the discretized right-hand-side
 93:       as a time-dependent matrix.
 94:   */
 95:   TSSetRHSFunction(ts,NULL,TSComputeRHSFunctionLinear,&appctx);
 96:   TSSetRHSJacobian(ts,NULL,NULL,RHSMatrixHeat,&appctx);
 97:   TSSetSolutionFunction(ts,(PetscErrorCode (*)(TS,PetscReal,Vec,void*))Solution,&appctx);

 99:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
100:      Customize timestepping solver:
101:        - Set timestepping duration info
102:      Then set runtime options, which can override these defaults.
103:      For example,
104:           -ts_max_steps <maxsteps> -ts_max_time <maxtime>
105:      to override the defaults set by TSSetMaxSteps()/TSSetMaxTime().
106:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

108:   DMDAGetInfo(da,PETSC_IGNORE,&M,0,0,0,0,0,0,0,0,0,0,0);
109:   dt   = .48/(M*M);
110:   TSSetTimeStep(ts,dt);
111:   TSSetMaxSteps(ts,1000);
112:   TSSetMaxTime(ts,100.0);
113:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
114:   TSSetType(ts,TSARKIMEX);
115:   TSSetFromOptions(ts);

117:   /*
118:      Evaluate initial conditions
119:   */
120:   InitialConditions(ts,U,&appctx);

122:   /*
123:      Run the timestepping solver
124:   */
125:   TSSolve(ts,U);

127:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
128:      Free work space.  All PETSc objects should be destroyed when they
129:      are no longer needed.
130:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

132:   TSDestroy(&ts);
133:   VecDestroy(&U);
134:   DMDestroy(&da);

136:   /*
137:      Always call PetscFinalize() before exiting a program.  This routine
138:        - finalizes the PETSc libraries as well as MPI
139:        - provides summary and diagnostic information if certain runtime
140:          options are chosen (e.g., -log_view).
141:   */
142:   PetscFinalize();
143:   return ierr;
144: }
145: /* --------------------------------------------------------------------- */
146: /*
147:    InitialConditions - Computes the solution at the initial time.

149:    Input Parameter:
150:    u - uninitialized solution vector (global)
151:    appctx - user-defined application context

153:    Output Parameter:
154:    u - vector with solution at initial time (global)
155: */
156: PetscErrorCode InitialConditions(TS ts,Vec U,AppCtx *appctx)
157: {
158:   PetscScalar    *u,h;
160:   PetscInt       i,mstart,mend,xm,M;
161:   DM             da;

163:   TSGetDM(ts,&da);
164:   DMDAGetCorners(da,&mstart,0,0,&xm,0,0);
165:   DMDAGetInfo(da,PETSC_IGNORE,&M,0,0,0,0,0,0,0,0,0,0,0);
166:   h    = 1.0/M;
167:   mend = mstart + xm;
168:   /*
169:     Get a pointer to vector data.
170:     - For default PETSc vectors, VecGetArray() returns a pointer to
171:       the data array.  Otherwise, the routine is implementation dependent.
172:     - You MUST call VecRestoreArray() when you no longer need access to
173:       the array.
174:     - Note that the Fortran interface to VecGetArray() differs from the
175:       C version.  See the users manual for details.
176:   */
177:   DMDAVecGetArray(da,U,&u);

179:   /*
180:      We initialize the solution array by simply writing the solution
181:      directly into the array locations.  Alternatively, we could use
182:      VecSetValues() or VecSetValuesLocal().
183:   */
184:   for (i=mstart; i<mend; i++) u[i] = PetscSinScalar(PETSC_PI*i*6.*h) + 3.*PetscSinScalar(PETSC_PI*i*2.*h);

186:   /*
187:      Restore vector
188:   */
189:   DMDAVecRestoreArray(da,U,&u);
190:   return 0;
191: }
192: /* --------------------------------------------------------------------- */
193: /*
194:    Solution - Computes the exact solution at a given time.

196:    Input Parameters:
197:    t - current time
198:    solution - vector in which exact solution will be computed
199:    appctx - user-defined application context

201:    Output Parameter:
202:    solution - vector with the newly computed exact solution
203: */
204: PetscErrorCode Solution(TS ts,PetscReal t,Vec U,AppCtx *appctx)
205: {
206:   PetscScalar    *u,ex1,ex2,sc1,sc2,h;
208:   PetscInt       i,mstart,mend,xm,M;
209:   DM             da;

211:   TSGetDM(ts,&da);
212:   DMDAGetCorners(da,&mstart,0,0,&xm,0,0);
213:   DMDAGetInfo(da,PETSC_IGNORE,&M,0,0,0,0,0,0,0,0,0,0,0);
214:   h    = 1.0/M;
215:   mend = mstart + xm;
216:   /*
217:      Get a pointer to vector data.
218:   */
219:   DMDAVecGetArray(da,U,&u);

221:   /*
222:      Simply write the solution directly into the array locations.
223:      Alternatively, we culd use VecSetValues() or VecSetValuesLocal().
224:   */
225:   ex1 = PetscExpScalar(-36.*PETSC_PI*PETSC_PI*appctx->d*t);
226:   ex2 = PetscExpScalar(-4.*PETSC_PI*PETSC_PI*appctx->d*t);
227:   sc1 = PETSC_PI*6.*h;                 sc2 = PETSC_PI*2.*h;
228:   for (i=mstart; i<mend; i++) u[i] = PetscSinScalar(sc1*(PetscReal)i + appctx->a*PETSC_PI*6.*t)*ex1 + 3.*PetscSinScalar(sc2*(PetscReal)i + appctx->a*PETSC_PI*2.*t)*ex2;

230:   /*
231:      Restore vector
232:   */
233:   DMDAVecRestoreArray(da,U,&u);
234:   return 0;
235: }

237: /* --------------------------------------------------------------------- */
238: /*
239:    RHSMatrixHeat - User-provided routine to compute the right-hand-side
240:    matrix for the heat equation.

242:    Input Parameters:
243:    ts - the TS context
244:    t - current time
245:    global_in - global input vector
246:    dummy - optional user-defined context, as set by TSetRHSJacobian()

248:    Output Parameters:
249:    AA - Jacobian matrix
250:    BB - optionally different preconditioning matrix
251:    str - flag indicating matrix structure

253:    Notes:
254:    Recall that MatSetValues() uses 0-based row and column numbers
255:    in Fortran as well as in C.
256: */
257: PetscErrorCode RHSMatrixHeat(TS ts,PetscReal t,Vec U,Mat AA,Mat BB,void *ctx)
258: {
259:   Mat            A       = AA;                /* Jacobian matrix */
260:   AppCtx         *appctx = (AppCtx*)ctx;     /* user-defined application context */
261:   PetscInt       mstart, mend;
263:   PetscInt       i,idx[3],M,xm;
264:   PetscScalar    v[3],h;
265:   DM             da;

267:   TSGetDM(ts,&da);
268:   DMDAGetInfo(da,0,&M,0,0,0,0,0,0,0,0,0,0,0);
269:   DMDAGetCorners(da,&mstart,0,0,&xm,0,0);
270:   h    = 1.0/M;
271:   mend = mstart + xm;
272:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
273:      Compute entries for the locally owned part of the matrix
274:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
275:   /*
276:      Set matrix rows corresponding to boundary data
277:   */

279:   /* diffusion */
280:   v[0] = appctx->d/(h*h);
281:   v[1] = -2.0*appctx->d/(h*h);
282:   v[2] = appctx->d/(h*h);
283:   if (!mstart) {
284:     idx[0] = M-1; idx[1] = 0; idx[2] = 1;
285:     MatSetValues(A,1,&mstart,3,idx,v,INSERT_VALUES);
286:     mstart++;
287:   }

289:   if (mend == M) {
290:     mend--;
291:     idx[0] = M-2; idx[1] = M-1; idx[2] = 0;
292:     MatSetValues(A,1,&mend,3,idx,v,INSERT_VALUES);
293:   }

295:   /*
296:      Set matrix rows corresponding to interior data.  We construct the
297:      matrix one row at a time.
298:   */
299:   for (i=mstart; i<mend; i++) {
300:     idx[0] = i-1; idx[1] = i; idx[2] = i+1;
301:     MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);
302:   }
303:   MatAssemblyBegin(A,MAT_FLUSH_ASSEMBLY);
304:   MatAssemblyEnd(A,MAT_FLUSH_ASSEMBLY);

306:   DMDAGetCorners(da,&mstart,0,0,&xm,0,0);
307:   mend = mstart + xm;
308:   if (!appctx->upwind) {
309:     /* advection -- centered differencing */
310:     v[0] = -.5*appctx->a/(h);
311:     v[1] = .5*appctx->a/(h);
312:     if (!mstart) {
313:       idx[0] = M-1; idx[1] = 1;
314:       MatSetValues(A,1,&mstart,2,idx,v,ADD_VALUES);
315:       mstart++;
316:     }

318:     if (mend == M) {
319:       mend--;
320:       idx[0] = M-2; idx[1] = 0;
321:       MatSetValues(A,1,&mend,2,idx,v,ADD_VALUES);
322:     }

324:     for (i=mstart; i<mend; i++) {
325:       idx[0] = i-1; idx[1] = i+1;
326:       MatSetValues(A,1,&i,2,idx,v,ADD_VALUES);
327:     }
328:   } else {
329:     /* advection -- upwinding */
330:     v[0] = -appctx->a/(h);
331:     v[1] = appctx->a/(h);
332:     if (!mstart) {
333:       idx[0] = 0; idx[1] = 1;
334:       MatSetValues(A,1,&mstart,2,idx,v,ADD_VALUES);
335:       mstart++;
336:     }

338:     if (mend == M) {
339:       mend--;
340:       idx[0] = M-1; idx[1] = 0;
341:       MatSetValues(A,1,&mend,2,idx,v,ADD_VALUES);
342:     }

344:     for (i=mstart; i<mend; i++) {
345:       idx[0] = i; idx[1] = i+1;
346:       MatSetValues(A,1,&i,2,idx,v,ADD_VALUES);
347:     }
348:   }

350:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
351:      Complete the matrix assembly process and set some options
352:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
353:   /*
354:      Assemble matrix, using the 2-step process:
355:        MatAssemblyBegin(), MatAssemblyEnd()
356:      Computations can be done while messages are in transition
357:      by placing code between these two statements.
358:   */
359:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
360:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

362:   /*
363:      Set and option to indicate that we will never add a new nonzero location
364:      to the matrix. If we do, it will generate an error.
365:   */
366:   MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
367:   return 0;
368: }

370: /*TEST

372:    test:
373:       args: -pc_type mg -da_refine 2  -ts_view  -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3
374:       requires: double
375:       filter: grep -v "total number of"

377:    test:
378:       suffix: 2
379:       args:  -pc_type mg -da_refine 2  -ts_view  -ts_monitor_draw_solution -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3
380:       requires: x
381:       output_file: output/ex3_1.out
382:       requires: double
383:       filter: grep -v "total number of"

385: TEST*/